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# 1.4 - PowerPoint PPT Presentation

1.4. FORMULAS FOR LINEAR FUNCTIONS. Finding a Formula for a Linear Function from a Table of Data. Example 1 The following table gives data from a linear function for a grapefruit thrown into the air. Find the formula for the function. Solution

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### 1.4

FORMULAS FOR LINEAR FUNCTIONS

Example 1

The following table gives data from a linear function for a grapefruit thrown into the air. Find the formula for the function.

Solution

We will look for a function of the form y = mx + b and begin by computing the slope:

Now we can determine b using m and the point (2, 16):

y = -32x+ b; 16 = -32 (2) + b which gives b = 80

So the formula for our function is

The following table gives data from a linear function. Find a formula for the function.

Solution

We will look for a function of the form y = mx + b and begin by computing the slope:

Now we can determine b using m and the point (32, 0):

y = 5/9 x + b; 0 = 5/9 (32) + b which gives b = -160/9

So the formula for our function is

Exercise 30

Solution

First we will find the slope of the line using (4, 7) and (12, 3).

We will look for a function of the form y – y0 = m(x – x0) using (4, 7)

y – 7 = – 0.5 (x – 4)

y – 7 = – 0.5x + 2

which simplifies to

y = – 0.5 x + 9

y

The graph gives data from a linear function. Find a formula for the function.

x

Example 3

We have \$24 to spend on soda and chips for a party. A six-pack of soda costs \$3 and a bag of chips costs \$2. The number of six-packs we can afford, s, is a function of the number of bags of chips we decide to buy, c.

• Find an equation relating s and c.

Solution

• The amount of money (\$) spent on soda will be 3s.

• The amount of money (\$) spent on chips will be 2c.

• Assuming we spend all \$24, the equation becomes:

2c + 3s = 24

3s = -2c + 24

s = – 2/3 c+ 8

Example 3

From (a), the equation is

(b) Graph the equation. Interpret the intercepts and the slope in the

context of the party.

Solution

All soda

No chips

The fact that m = −2/3 means that for each additional bag of chips purchased, we can purchase 2/3 fewer six-packs of soda.

6 packs of soda and 4 bags of chips

All chips

No soda

Alternative Forms for Descriptionthe Equation of a Line

• The slope-interceptform is

y = mx + b

where m is the slope and b is the y-intercept.

• The point-slope form is

y − y0 = m(x − x0)

where m is the slope and (x0, y0) is a point on the line.

• The standard form is

Ax + By + C = 0

where A, B, and C are constants.